Note

You can download this example as a Jupyter notebook or start it in interactive mode.

Simple electricity market examples#

This example gradually builds up more and more complicated energy-only electricity markets in PyPSA, starting from a single bidding zone, going up to multiple bidding zones connected with transmission (NTCs) along with variable renewables and storage.

Preliminaries#

Here libraries are imported and data is defined.

[1]:
import pypsa, numpy as np
ERROR 1: PROJ: proj_create_from_database: Open of /home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/latest/share/proj failed
[2]:
# marginal costs in EUR/MWh
marginal_costs = {"Wind": 0, "Hydro": 0, "Coal": 30, "Gas": 60, "Oil": 80}

# power plant capacities (nominal powers in MW) in each country (not necessarily realistic)
power_plant_p_nom = {
    "South Africa": {"Coal": 35000, "Wind": 3000, "Gas": 8000, "Oil": 2000},
    "Mozambique": {
        "Hydro": 1200,
    },
    "Swaziland": {
        "Hydro": 600,
    },
}

# transmission capacities in MW (not necessarily realistic)
transmission = {
    "South Africa": {"Mozambique": 500, "Swaziland": 250},
    "Mozambique": {"Swaziland": 100},
}

# country electrical loads in MW (not necessarily realistic)
loads = {"South Africa": 42000, "Mozambique": 650, "Swaziland": 250}

Single bidding zone with fixed load, one period#

In this example we consider a single market bidding zone, South Africa.

The inelastic load has essentially infinite marginal utility (or higher than the marginal cost of any generator).

[3]:
country = "South Africa"

network = pypsa.Network()

network.add("Bus", country)

for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        "{} {}".format(country, tech),
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
    )


network.add("Load", "{} load".format(country), bus=country, p_set=loads[country])
[4]:
# Run optimisation to determine market dispatch
network.optimize()
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.02s
INFO:linopy.solvers:GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-gcf96raz.lp --output /tmp/linopy-solve-wdm4ilkl.sol
Reading problem data from '/tmp/linopy-problem-gcf96raz.lp'...
9 rows, 4 columns, 12 non-zeros
56 lines were read
GLPK Simplex Optimizer 5.0
9 rows, 4 columns, 12 non-zeros
Preprocessing...
1 row, 3 columns, 3 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 1
      0: obj =   1.260000000e+06 inf =   7.000e+03 (1)
      1: obj =   1.470000000e+06 inf =   0.000e+00 (0)
*     2: obj =   1.290000000e+06 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (40400 bytes)
Writing basic solution to '/tmp/linopy-solve-wdm4ilkl.sol'...

INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 4 primals, 9 duals
Objective: 1.29e+06
Solver model: not available
Solver message: optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper were not assigned to the network.
[4]:
('ok', 'optimal')
[5]:
# print the load active power (P) consumption
network.loads_t.p
[5]:
Load South Africa load
snapshot
now 42000.0
[6]:
# print the generator active power (P) dispatch
network.generators_t.p
[6]:
Generator South Africa Coal South Africa Wind South Africa Gas South Africa Oil
snapshot
now 35000.0 3000.0 4000.0 0.0
[7]:
# print the clearing price (corresponding to gas)
network.buses_t.marginal_price
[7]:
Bus South Africa
snapshot
now 60.0

Two bidding zones connected by transmission, one period#

In this example we have bidirectional transmission capacity between two bidding zones. The power transfer is treated as controllable (like an A/NTC (Available/Net Transfer Capacity) or HVDC line). Note that in the physical grid, power flows passively according to the network impedances.

[8]:
network = pypsa.Network()

countries = ["Mozambique", "South Africa"]

for country in countries:
    network.add("Bus", country)

    for tech in power_plant_p_nom[country]:
        network.add(
            "Generator",
            "{} {}".format(country, tech),
            bus=country,
            p_nom=power_plant_p_nom[country][tech],
            marginal_cost=marginal_costs[tech],
        )

    network.add("Load", "{} load".format(country), bus=country, p_set=loads[country])

    # add transmission as controllable Link
    if country not in transmission:
        continue

    for other_country in countries:
        if other_country not in transmission[country]:
            continue

        # NB: Link is by default unidirectional, so have to set p_min_pu = -1
        # to allow bidirectional (i.e. also negative) flow
        network.add(
            "Link",
            "{} - {} link".format(country, other_country),
            bus0=country,
            bus1=other_country,
            p_nom=transmission[country][other_country],
            p_min_pu=-1,
        )
[9]:
network.optimize()
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.02s
INFO:linopy.solvers:GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-hl5hiiaw.lp --output /tmp/linopy-solve-c2n1107a.sol
Reading problem data from '/tmp/linopy-problem-hl5hiiaw.lp'...
14 rows, 6 columns, 19 non-zeros
78 lines were read
GLPK Simplex Optimizer 5.0
14 rows, 6 columns, 19 non-zeros
Preprocessing...
1 row, 4 columns, 4 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 1
      0: obj =   1.245000000e+06 inf =   6.500e+03 (1)
      1: obj =   1.440000000e+06 inf =   0.000e+00 (0)
*     2: obj =   1.260000000e+06 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (40404 bytes)
Writing basic solution to '/tmp/linopy-solve-c2n1107a.sol'...

INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 6 primals, 14 duals
Objective: 1.26e+06
Solver model: not available
Solver message: optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Link-fix-p-lower, Link-fix-p-upper were not assigned to the network.
[9]:
('ok', 'optimal')
[10]:
network.loads_t.p
[10]:
Load Mozambique load South Africa load
snapshot
now 650.0 42000.0
[11]:
network.generators_t.p
[11]:
Generator Mozambique Hydro South Africa Coal South Africa Wind South Africa Gas South Africa Oil
snapshot
now 1150.0 35000.0 3000.0 3500.0 0.0
[12]:
network.links_t.p0
[12]:
Link South Africa - Mozambique link
snapshot
now -500.0
[13]:
# print the clearing price (corresponding to water in Mozambique and gas in SA)
network.buses_t.marginal_price
[13]:
Bus Mozambique South Africa
snapshot
now 0.0 60.0
[14]:
# link shadow prices
network.links_t.mu_lower
[14]:
Link
snapshot
now

Three bidding zones connected by transmission, one period#

In this example we have bidirectional transmission capacity between three bidding zones. The power transfer is treated as controllable (like an A/NTC (Available/Net Transfer Capacity) or HVDC line). Note that in the physical grid, power flows passively according to the network impedances.

[15]:
network = pypsa.Network()

countries = ["Swaziland", "Mozambique", "South Africa"]

for country in countries:
    network.add("Bus", country)

    for tech in power_plant_p_nom[country]:
        network.add(
            "Generator",
            "{} {}".format(country, tech),
            bus=country,
            p_nom=power_plant_p_nom[country][tech],
            marginal_cost=marginal_costs[tech],
        )

    network.add("Load", "{} load".format(country), bus=country, p_set=loads[country])

    # add transmission as controllable Link
    if country not in transmission:
        continue

    for other_country in countries:
        if other_country not in transmission[country]:
            continue

        # NB: Link is by default unidirectional, so have to set p_min_pu = -1
        # to allow bidirectional (i.e. also negative) flow
        network.add(
            "Link",
            "{} - {} link".format(country, other_country),
            bus0=country,
            bus1=other_country,
            p_nom=transmission[country][other_country],
            p_min_pu=-1,
        )
[16]:
network.optimize()
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.02s
INFO:linopy.solvers:GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-lzhr5hx2.lp --output /tmp/linopy-solve-rnult3p8.sol
Reading problem data from '/tmp/linopy-problem-lzhr5hx2.lp'...
21 rows, 9 columns, 30 non-zeros
113 lines were read
GLPK Simplex Optimizer 5.0
21 rows, 9 columns, 30 non-zeros
Preprocessing...
3 rows, 6 columns, 9 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 3
      0: obj =   1.237500000e+06 inf =   6.250e+03 (1)
      1: obj =   1.425000000e+06 inf =   0.000e+00 (0)
*     2: obj =   1.245000000e+06 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (40424 bytes)
Writing basic solution to '/tmp/linopy-solve-rnult3p8.sol'...

INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 9 primals, 21 duals
Objective: 1.24e+06
Solver model: not available
Solver message: optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Link-fix-p-lower, Link-fix-p-upper were not assigned to the network.
[16]:
('ok', 'optimal')
[17]:
network.loads_t.p
[17]:
Load Swaziland load Mozambique load South Africa load
snapshot
now 250.0 650.0 42000.0
[18]:
network.generators_t.p
[18]:
Generator Swaziland Hydro Mozambique Hydro South Africa Coal South Africa Wind South Africa Gas South Africa Oil
snapshot
now 600.0 1050.0 35000.0 3000.0 3250.0 0.0
[19]:
network.links_t.p0
[19]:
Link Mozambique - Swaziland link South Africa - Swaziland link South Africa - Mozambique link
snapshot
now -100.0 -250.0 -500.0
[20]:
# print the clearing price (corresponding to hydro in S and M, and gas in SA)
network.buses_t.marginal_price
[20]:
Bus Swaziland Mozambique South Africa
snapshot
now 0.0 0.0 60.0
[21]:
# link shadow prices
network.links_t.mu_lower
[21]:
Link
snapshot
now

Single bidding zone with price-sensitive industrial load, one period#

In this example we consider a single market bidding zone, South Africa.

Now there is a large industrial load with a marginal utility which is low enough to interact with the generation marginal cost.

[22]:
country = "South Africa"

network = pypsa.Network()

network.add("Bus", country)

for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        "{} {}".format(country, tech),
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
    )

# standard high marginal utility consumers
network.add("Load", "{} load".format(country), bus=country, p_set=loads[country])

# add an industrial load as a dummy negative-dispatch generator with marginal utility of 70 EUR/MWh for 8000 MW
network.add(
    "Generator",
    "{} industrial load".format(country),
    bus=country,
    p_max_pu=0,
    p_min_pu=-1,
    p_nom=8000,
    marginal_cost=70,
)
[23]:
network.optimize()
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.01s
INFO:linopy.solvers:GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-52t2aa46.lp --output /tmp/linopy-solve-8darm1u0.sol
Reading problem data from '/tmp/linopy-problem-52t2aa46.lp'...
11 rows, 5 columns, 15 non-zeros
67 lines were read
GLPK Simplex Optimizer 5.0
11 rows, 5 columns, 15 non-zeros
Preprocessing...
1 row, 4 columns, 4 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 1
      0: obj =   9.400000000e+05 inf =   1.500e+04 (1)
      3: obj =   1.480000000e+06 inf =   0.000e+00 (0)
*     5: obj =   1.250000000e+06 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (40404 bytes)
Writing basic solution to '/tmp/linopy-solve-8darm1u0.sol'...

INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 5 primals, 11 duals
Objective: 1.25e+06
Solver model: not available
Solver message: optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper were not assigned to the network.
[23]:
('ok', 'optimal')
[24]:
network.loads_t.p
[24]:
Load South Africa load
snapshot
now 42000.0
[25]:
# NB only half of industrial load is served, because this maxes out
# Gas. Oil is too expensive with a marginal cost of 80 EUR/MWh
network.generators_t.p
[25]:
Generator South Africa Coal South Africa Wind South Africa Gas South Africa Oil South Africa industrial load
snapshot
now 35000.0 3000.0 8000.0 0.0 -4000.0
[26]:
network.buses_t.marginal_price
[26]:
Bus South Africa
snapshot
now 70.0

Single bidding zone with fixed load, several periods#

In this example we consider a single market bidding zone, South Africa.

We consider multiple time periods (labelled [0,1,2,3]) to represent variable wind generation.

[27]:
country = "South Africa"

network = pypsa.Network()

# snapshots labelled by [0,1,2,3]
network.set_snapshots(range(4))

network.add("Bus", country)

# p_max_pu is variable for wind
for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        "{} {}".format(country, tech),
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
        p_max_pu=([0.3, 0.6, 0.4, 0.5] if tech == "Wind" else 1),
    )

# load which varies over the snapshots
network.add(
    "Load",
    "{} load".format(country),
    bus=country,
    p_set=loads[country] + np.array([0, 1000, 3000, 4000]),
)
[28]:
network.optimize()
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.02s
INFO:linopy.solvers:GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-19ybwm50.lp --output /tmp/linopy-solve-2fd2vjho.sol
Reading problem data from '/tmp/linopy-problem-19ybwm50.lp'...
36 rows, 16 columns, 48 non-zeros
194 lines were read
GLPK Simplex Optimizer 5.0
36 rows, 16 columns, 48 non-zeros
Preprocessing...
4 rows, 12 columns, 12 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 4
      0: obj =   5.280000000e+06 inf =   3.600e+04 (4)
      7: obj =   6.380000000e+06 inf =   0.000e+00 (0)
*    13: obj =   6.082000000e+06 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (48739 bytes)
Writing basic solution to '/tmp/linopy-solve-2fd2vjho.sol'...

INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 16 primals, 36 duals
Objective: 6.08e+06
Solver model: not available
Solver message: optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper were not assigned to the network.
[28]:
('ok', 'optimal')
[29]:
network.loads_t.p
[29]:
Load South Africa load
snapshot
0 42000.0
1 43000.0
2 45000.0
3 46000.0
[30]:
network.generators_t.p
[30]:
Generator South Africa Coal South Africa Wind South Africa Gas South Africa Oil
snapshot
0 35000.0 900.0 6100.0 0.0
1 35000.0 1800.0 6200.0 0.0
2 35000.0 1200.0 8000.0 800.0
3 35000.0 1500.0 8000.0 1500.0
[31]:
network.buses_t.marginal_price
[31]:
Bus South Africa
snapshot
0 60.0
1 60.0
2 80.0
3 80.0

Single bidding zone with fixed load and storage, several periods#

In this example we consider a single market bidding zone, South Africa.

We consider multiple time periods (labelled [0,1,2,3]) to represent variable wind generation. Storage is allowed to do price arbitrage to reduce oil consumption.

[32]:
country = "South Africa"

network = pypsa.Network()

# snapshots labelled by [0,1,2,3]
network.set_snapshots(range(4))

network.add("Bus", country)

# p_max_pu is variable for wind
for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        "{} {}".format(country, tech),
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
        p_max_pu=([0.3, 0.6, 0.4, 0.5] if tech == "Wind" else 1),
    )

# load which varies over the snapshots
network.add(
    "Load",
    "{} load".format(country),
    bus=country,
    p_set=loads[country] + np.array([0, 1000, 3000, 4000]),
)

# storage unit to do price arbitrage
network.add(
    "StorageUnit",
    "{} pumped hydro".format(country),
    bus=country,
    p_nom=1000,
    max_hours=6,  # energy storage in terms of hours at full power
)
[33]:
network.optimize()
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.04s
INFO:linopy.solvers:GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-jydh5xt7.lp --output /tmp/linopy-solve-m7spgrt4.sol
Reading problem data from '/tmp/linopy-problem-jydh5xt7.lp'...
64 rows, 28 columns, 95 non-zeros
330 lines were read
GLPK Simplex Optimizer 5.0
64 rows, 28 columns, 95 non-zeros
Preprocessing...
8 rows, 23 columns, 34 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 8
      0: obj =   5.280000000e+06 inf =   3.600e+04 (4)
      7: obj =   6.380000000e+06 inf =   0.000e+00 (0)
*    17: obj =   6.046000000e+06 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (72636 bytes)
Writing basic solution to '/tmp/linopy-solve-m7spgrt4.sol'...

INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 28 primals, 64 duals
Objective: 6.05e+06
Solver model: not available
Solver message: optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, StorageUnit-fix-p_dispatch-lower, StorageUnit-fix-p_dispatch-upper, StorageUnit-fix-p_store-lower, StorageUnit-fix-p_store-upper, StorageUnit-fix-state_of_charge-lower, StorageUnit-fix-state_of_charge-upper, StorageUnit-energy_balance were not assigned to the network.
[33]:
('ok', 'optimal')
[34]:
network.loads_t.p
[34]:
Load South Africa load
snapshot
0 42000.0
1 43000.0
2 45000.0
3 46000.0
[35]:
network.generators_t.p
[35]:
Generator South Africa Coal South Africa Wind South Africa Gas South Africa Oil
snapshot
0 35000.0 900.0 6900.0 0.0
1 35000.0 1800.0 7200.0 0.0
2 35000.0 1200.0 8000.0 0.0
3 35000.0 1500.0 8000.0 500.0
[36]:
network.storage_units_t.p
[36]:
StorageUnit South Africa pumped hydro
snapshot
0 -800.0
1 -1000.0
2 800.0
3 1000.0
[37]:
network.storage_units_t.state_of_charge
[37]:
StorageUnit South Africa pumped hydro
snapshot
0 800.0
1 1800.0
2 1000.0
3 0.0
[38]:
network.buses_t.marginal_price
[38]:
Bus South Africa
snapshot
0 60.0
1 60.0
2 60.0
3 80.0